1. Field of the Invention
This invention relates in general to electrical circuits which provide smoothly varying non-linear transfer functions, and in particular to circuits for use in producing a linear, differentiatable waveform from a waveform having a logarithmically varying portion.
2. Description of the Prior Art
In many applications, it is desirable to transform a signal or waveform from one scale to another. In some cases, for instance, it is desirable to produce a linear signal from a signal which varies logarithmically. One such application, for example, involves aircraft radio altimeter signal processing. As is well known, radio altimeters are designed in accordance with ARINC specifications to produce an output signal which varies linearly over the lower portion of the altitude range and logarithmically over the upper portion. When the signal is applied to a cockpit indicator, the linear portion is displayed over a large region of an indicator dial, and represents lower altitudes where precision is particularly important. The logarithmically varying portion, on the other hand, is compressed into a smaller region of the indicator dial, and indicates higher altitudes at which precise accuracy is not of such importance.
It is sometimes desirable to develop a linear altitude signal from the normal radio altimeter signal just described. For instance, in automatic flight control systems in which certain aircraft control surfaces are controlled automatically in response to various air data and sensor signals, it may be desirable to have a linear altitude signal over a range of radio altimeter indications of interest.
One prior art system to obtain such linear signal waveform is shown in U.S. Pat. No. 3,974,365. This system produces a linear signal representation of the signal having a logarithmic section, with less than five percent error. This circuit represents one method for linearizing data, which is especially useful to enable differentiation of the signal to obtain a signal indicative of the rate of change of altitude, a parameter which is also important in automatic flight control systems and the like.
In many scale transforming circuits, however, the transfer function of the circuit used to derive the linear signal is approximated by a number of segments. At the so-called "breakpoints" or regions at which two adjacent segments join, a sharp transition may occur. In applications where the approximated signal is differentiated, such as in derivation of a rate of altitude change signal from an altitude signal, differentiation at such "breakpoints" often introduces large errors in the differentiated signal. Consequently, it is desirable that the signal to be differentiated be as smooth as possible over its range of interest, and especially at the "breakpoint" regions.
The present invention, in general, is intended for use in such scale conversion, and in particular, is directed to linearizing a radio altimeter signal which may vary logarithmically over a portion of the altitude range of interest. The circuit in accordance with the invention can be used in combination with, or in some instances to replace entirely, the system of the aforementioned prior art patents.